Hello,
I am looking into filter behaviour in signal processing. To do so
I make use of LaplaceTransform and InverseLaplaceTransform.
When I want results to be evaluated as in Plots I get problems
from the transform with numerical computation error messages and
warnings.
I define:
In[1]:= <<Calculus`LaplaceTransform`
In[2]:= om[t_]:= If[t>0,1,0]
In[3]:= q[s_] := LaplaceTransform[om[t],t,s]
In[4]:= Plot[q[s],{s,0,100}]
And get :
1
Power::infy: Infinite expression -- encountered.
0.
1
Power::infy: Infinite expression -- encountered.
0.
1
Power::infy: Infinite expression -- encountered.
0.
General::stop: Further output of Power::infy
will be suppressed during this calculation.
NIntegrate::precw:
Warning: The precision of the argument function (
Exp[-(0. t)] If[t > 0, 1.1, 1]) is less than WorkingPrecision (16).
NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following:
singularity, oscillatory integrand, or insufficient WorkingPrecision.
NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after 7
56
recursive bisections in t near t = 2.28833 10 .
NIntegrate::precw:
Warning: The precision of the argument function (
Exp[-(0. t)] If[t > 0, 1.1, 1]) is less than WorkingPrecision (16).
NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following:
singularity, oscillatory integrand, or insufficient WorkingPrecision.
NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after 7
56
recursive bisections in t near t = 2.28833 10 .
Plot::plnr: CompiledFunction[{s}, q[s], -CompiledCode-][s]
is not a machine-size real number at s = 0..
General::ovfl: Overflow occurred in computation.
General::ovfl: Overflow occurred in computation.
General::ovfl: Overflow occurred in computation.
General::stop: Further output of General::ovfl
will be suppressed during this calculation.
The plot I finally get doesn't look like what I expected
a simple switch in frequency.
I think the problem comes from the integration in the transform.
Normally it is done from -infinity to +infinity. With a finite
set of data I would like to reduce this range.
Perhaps then also the result of the transform would become better
I would like to hear comments about these thoughts.
Gert Gottschalk
gottsch at mikro.ee.tu-berlin.de
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